Problem: What's the first wrong statement in the proof below that $ \triangle DEB \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle ECF \cong \angle BDE$ $, \ $ $ \overline{CF} \cong \overline{BD}$ $, \ $ $ \angle CFE \cong \angle DBE$ $, \ $ $ \overline{AC} \cong \overline{DE}$ $, \ $ $ \angle ACB \cong \angle BDE$ $, \ $ and $\ $ $ \angle ABC \cong \angle DBE$ Proof $ \triangle DEB \cong \triangle CEF$ because ASA $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \overline{AD} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle DEB \cong \triangle CAB$ because AAS $ \triangle DEB \cong \triangle CEB$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{BE} \cong \overline{AD}$ is the first wrong statement.